QUICK SEARCH:   [advanced] Author: Keyword(s):
Home     Help     Feedback     Subscriptions     Archive     Search     Table of Contents

This Article Summary Full Text Full Text (PDF) Alert me when this article is cited Alert me if a correction is posted Services Email this article to a friend Similar articles in this journal Similar articles in PubMed Alert me to new issues of the journal Download to citation manager Citing Articles Citing Articles via HighWire Citing Articles via Google Scholar Google Scholar Articles by Sun, M. Articles by Tang, J. Search for Related Content PubMed PubMed Citation Articles by Sun, M. Articles by Tang, J.

Lift and power requirements of hovering flight in Drosophila virilis

Mao Sun^* and Jian Tang

Institute of Fluid Mechanics, Beijing University of Aeronautics and Astronautics, Beijing 100083, People's Republic of China

View larger version (15K): [in a new window]   Fig. 1. Sketches of the reference frames and wing motion. (A) OXYZ is an inertial frame, with the XY plane in the stroke plane. oxyz is a frame fixed on the wing, with the x axis along the wing chord, and the y axis along the wing span. is the azimuthal angle of the wing, is the angle of attack and R is the wing length. (B) The motion of a section of the wing.

View larger version (117K): [in a new window]   Fig. 2. The wing planform and a portion of the body-conforming grid near the wing in the z=0 plane (see Fig. 1A for a definition of this plane).

View larger version (7K): [in a new window]   Fig. 3. Diagram showing how the moments and product of inertia are computed. o, x, y, coordinates in wing-fixed frame of reference; dmw, mass element of the wing; r, vector distance between point o and a mass element of the wing; i, j, unit vectors in the x and y directions, respectively.

View larger version (23K): [in a new window]   Fig. 4. Comparison of the calculated lift coefficient CL with the measured CL. The experimental data are reproduced from Fig. 3 of Dickinson et al. (1999). (A) Advanced rotation. (B) Symmetrical rotation. (C) Delayed rotation. , non-dimensional time; c, non-dimensional period of one flapping cycle.

View larger version (8K): [in a new window]   Fig. 6. Mean lift coefficient versus midstroke angle of attack m (symmetrical rotation, non-dimensional duration of wing rotation r=0.36c, where c is the non-dimensional period of one flapping cycle).

View larger version (20K): [in a new window]   Fig. 7. Non-dimensional angular velocity of pitching rotation and azimuthal rotation (A), aerodynamic (B) and inertial (C) torque coefficients for translation (CQ,a,t, and CQ,i,t, respectively) and rotation (CQ,a,r and CQ,i,r, respectively) versus time during one cycle (midstroke angle of attack m=35°, symmetrical rotation, non-dimensional duration of wing rotation r=0.36c). c, non-dimensional period of one flapping cycle; , non-dimensional time.

View larger version (17K): [in a new window]   Fig. 8. The power coefficients for translation (CP,t) and rotation (CP,r) versus time during one cycle (midstroke angle of attack m=35°, symmetrical rotation, non-dimensional duration of wing rotation r=0.36c). c, non-dimensional period of one flapping cycle; , non-dimensional time.

View larger version (25K): [in a new window]   Fig. 9. Non-dimensional angular velocity of pitching rotation and azimuthal rotation (A), lift coefficient CL (B) and drag coefficient CD (C) versus time during one cycle for three different timings of wing rotation (midstroke angle of attack m=35°, non-dimensional duration of wing rotation r=0.36c). c, non-dimensional period of one flapping cycle; , non-dimensional time.

View larger version (25K): [in a new window]   Fig. 12. The power coefficients for translation (CP,t) and rotation (CP,r) versus time during one cycle for the different wing rotation timings (midstroke angle of attack m=35°, non-dimensional duration of wing rotation r=0.36c). c, non-dimensional period of one flapping cycle; , non-dimensional time.

View larger version (24K): [in a new window]   Fig. 5. Non-dimensional angular velocity of pitching rotation and azimuthal rotation (A), lift coefficient CL (B) and drag coefficient CD (C) versus time during one cycle for three midstroke angles of attack m (symmetrical rotation, non-dimensional duration of wing rotation r=0.36c). c, non-dimensional period of one flapping cycle; , non-dimensional time.

View larger version (18K): [in a new window]   Fig. 10. Non-dimensional angular velocity of pitching rotation and azimuthal rotation (A), aerodynamic (B) and inertial (C) torque coefficients for translation (CQ,a,t and CQ,i,t, respectively) and rotation (CQ,a,r and CQ,i,r, respectively) versus time during one cycle (midstroke angle of attack m=35°, advanced rotation, non-dimensional duration of wing rotation r=0.36c). c, non-dimensional period of one flapping cycle; , non-dimensional time.

View larger version (18K): [in a new window]   Fig. 11. Non-dimensional angular velocity of pitching rotation and azimuthal rotation (A), aerodynamic (B) and inertial (C) torque coefficients for translation (CQ,a,t and CQ,i,t, respectively) and rotation (CQ,a,r and CQ,i,r, respectively) versus time during one cycle (midstroke angle of attack m=35°, delayed rotation, non-dimensional duration of wing rotation r=0.36c). c, non-dimensional period of one flapping cycle; , non-dimensional time.

View larger version (27K): [in a new window]   Fig. 13. Non-dimensional angular velocity of pitching rotation and azimuthal rotation (A), lift coefficient CL (B) and drag coefficient CD (C) versus time during one cycle for three different values of the non-dimensional duration of wing rotation r. Symmetrical rotation; mean lift coefficient (midstroke angle of attack m was adjusted to make the mean lift equal to insect weight). c, non-dimensional period of one flapping cycle; , non-dimensional time.

View larger version (25K): [in a new window]   Fig. 14. The power coefficients for translation (CP,t) and rotation (CP,r) versus time during one cycle for three different values of the non-dimensional duration of wing rotation r. Symmetrical rotation; midstroke angle of attack m was adjusted to make the mean lift equal to insect weight. c, non-dimensional period of one flapping cycle; , non-dimensional time.